Critical points

Abstract

In section 2.2 we saw that linearisation in a neighbourhood of a critical point of an autonomous system $\dot{x} = f(x)$ leads to the equation

$$ \dot{y} = Ay $$

((3.1))

with A constant n × n-matrix; in this formulation the critical point has been translated to the origin. We exclude in this chapter the case of a singular matrix A, so

$$ \det A \ne 0. $$

.